"Riku is so quiet today."
Yuki said with curiosity.
"Are you feeling okay?"
Riku shook his head. "No, yesterday Aoi-senpai told me that my statements have low information content."
"That's harsh," Yuki laughed.
Aoi defended. "That's a misunderstanding. Precisely, I said 'overly predictable statements have low information content.'"
"Same thing."
"Different. In information theory, information content is measured by the magnitude of surprise."
Yuki opened her notebook. "Surprise?"
"Yes. Expected events have information content close to zero. The more unexpected the event, the greater the information content."
Aoi wrote an equation on the whiteboard.
"I(x) = -log₂ P(x)"
"The lower the probability, the greater the information content."
Riku began to understand. "So when I say my usual stupid things, it's not surprising, so information content is zero?"
"Unfortunately, yes," Aoi admitted. "But if Riku suddenly said something philosophical, the information content would be enormous."
"Because the probability is extremely low," Yuki supplemented.
Riku pondered. "So communication is about giving surprise?"
"Deep question," Aoi became serious. "Actually, surprise alone isn't sufficient."
"What do you mean?"
"Completely random words are indeed full of surprise. But they're meaningless."
Yuki gave an example. "Like saying 'apple quantum Tuesday' would just be confusing."
"Right. Communication requires shared context. Appropriate surprise within that context becomes information."
Aoi drew a diagram.
"Too predictable ← optimal surprise → too random"
"The middle is good communication."
Riku raised his hand. "Then I'll say something surprising now. Evaluate it."
"Go ahead."
Riku said with a serious face. "Entropy is the expected value of surprise."
For a moment, silence flowed.
"Huh?" Yuki was surprised.
Aoi's eyes widened too. "Riku, where did you learn that?"
"I secretly read your book yesterday."
"High information content," Aoi acknowledged. "Probabilistically quite a low-probability statement."
Yuki laughed. "But I'm really surprised. Is this information?"
"Yes. Surprise itself is information. But..."
"But?"
"Only when there's someone who can share the surprise does it become information."
Aoi continued. "There's a concept called mutual information. The amount of information two variables share."
"Like shared understanding between friends?" Riku asked.
"Close. The degree to which the other's statement reduces your uncertainty."
Yuki summarized. "So just giving surprise isn't enough. Surprise within the range the other can understand is important."
"Perfect understanding."
Riku said happily. "Then was my statement just now optimal?"
"Well, not bad," Aoi smiled. "But from now on, use it more naturally. According to context."
"Got it."
Yuki thought. "Sharing surprise is communication—such a wonderful way of thinking."
"The essence of information theory. Information is knowing what you didn't know. Sharing surprise."
"Conversations with appropriate surprise are more fun than predictable ones," Riku realized.
"But too much surprise is also tiring," Aoi cautioned.
"Balance is important."
The three laughed. Today's club room conversation was full of appropriate surprise. That was generating information.